What does the prefix 'ab-' mean in the Latin verb 'abundare'?

Question

abound (v.)
early 14c., from Old French abonder "to abound, be abundant, come together in great numbers" (12c.),
from Latin abundare "overflow, run over,"
from Latin ab- "off" (see ab-) + undare "rise in a wave," from unda "water, wave" (see water (n.1)).

What is the meaning of "off", while during a "rise in a wave"? Is there some hypotaxis?

I don't understand Prof. John Lawler's example with coffee sloshing in a cup held by walkers:

Ever tried to walk fast carrying a full cup of coffee? The coffee rises in waves set off by the motion and sloshes over from the top of the cup, if you're not careful. BTW, hypotaxis is a literary term, not a linguistic one. You've got to stop trying to learn grammar from a dictionary. Greek terms were coined for Greek by ancient Greek grammarians, who had extremely odd notions about language (where 'language' = 'Homeric Greek'; other people spoke barbaric languages, not real ones), and are rarely useful. But they do impress people, for sure.

Answer 1

Unda is a noun meaning "wave" (in a liquid). This led to a verb undāre, "to rise in a wave" as your dictionary put it, or I would say "to have waves".

Lawler was right on the mark. Consider liquid in a container. Move the container around and you get waves. If the waves get high enough, the liquid spills out of the container.

(Lawler is also right in saying that hypotaxis has nothing to do with this. Hypotaxis is the Greek literary term that encompasses several different linguistic ideas, but afaik all of them have to do with syntax. It's not meaningful to talk about hypotaxis in a single word.)

EDIT: To clarify, if liquid spills out, it's moving out and away from its container, hence ab.

Answer 2

The Latin verb means quite literally "flow over". When a liquid is spilled from ("from" = ab-) a container, it flows over the edges and waves away from its vessel. Spilling means going over an edge, and that requires creating a sufficiently high wave. Spilling also means having too much. I see no problem connecting the ab- with the listed meanings of abundare and descendants; the literal meaning is what ab- and unda suggest, and the rest seems natural.